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# A bookstore has a shelf that contains biographies which

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Intern
Joined: 18 Oct 2012
Posts: 7
A bookstore has a shelf that contains biographies which  [#permalink]

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Updated on: 22 Oct 2012, 08:56
4
00:00

Difficulty:

55% (hard)

Question Stats:

72% (03:03) correct 28% (03:15) wrong based on 58 sessions

A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for$12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries? (A) 9 (B) 10 (C) 13 (D) 22 (E) 25 Originally posted by Anichka on 22 Oct 2012, 03:46. Last edited by Bunuel on 22 Oct 2012, 08:56, edited 1 time in total. Renamed the topic. VP Joined: 02 Jul 2012 Posts: 1184 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Discounted books in a store [#permalink] ### Show Tags 22 Oct 2012, 04:45 1 Anichka wrote: A bookstore has a shelf that contains biographies which normally sell for$20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of$19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?

(A) 9
(B) 10
(C) 13
(D) 22
(E) 25

Let B be the discount on biographies and M be the discount on mysteries

So., B + M = 0.35 -----(1)

And

(20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19

--> 100(1-(1-B)) + 36(1-(1-M) = 19

100B + 36M = 19 ------(2)

Solving 1 & 2., we get M = 0.25 = 25%
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Joined: 18 Oct 2012
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Re: Discounted books in a store  [#permalink]

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22 Oct 2012, 06:03
Thanks! It works out now.

I have though a question.
In the problem it says: "The biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries." Doesn't that mean that when 5 biographies and 3 mysteries are purchased, the total amount will be 19 less than if the books have not been discounted, meaning, 5*20 + 3*12 = 136 (this would be if they kept the original price). But after the discount ( (5*20 - 5*20*b%) + (3*12 - 3*12*m%) = 136 - 19. Then, the equation doesn't work. Thank you for your reply! VP Joined: 02 Jul 2012 Posts: 1184 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Discounted books in a store [#permalink] ### Show Tags 22 Oct 2012, 07:45 1 Anichka wrote: Thanks! It works out now. I have though a question. In the problem it says: "The biographies and mysteries are discounted at different rates so that a customer saves a total of$19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries."

Doesn't that mean that when 5 biographies and 3 mysteries are purchased, the total amount will be 19 less than if the books have not been discounted, meaning, 5*20 + 3*12 = 136 (this would be if they kept the original price). But after the discount ( (5*20 - 5*20*b%) + (3*12 - 3*12*m%) = 136 - 19.
Then, the equation doesn't work.

You should note that it should be 5*20*(1-b) and 3*12*(1-m). To make it more clear.

Suppose an item costs $100. And now I am going to give a discount of 20%. The new price would not be$20 (i.e 100*0.2) rather it would be $80 (i.e 100*(1-0.2)). When you are discounting a price P by x%, the discounted price will be $$P*(1 - \frac{x}{100})$$ and not $$\frac{P*x}{100}$$ Kudos Please... If my post helped. _________________ Did you find this post helpful?... Please let me know through the Kudos button. Thanks To The Almighty - My GMAT Debrief GMAT Reading Comprehension: 7 Most Common Passage Types Director Joined: 22 Mar 2011 Posts: 601 WE: Science (Education) Re: Discounted books in a store [#permalink] ### Show Tags 22 Oct 2012, 08:02 1 Anichka wrote: A bookstore has a shelf that contains biographies which normally sell for$20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of$19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?

(A) 9
(B) 10
(C) 13
(D) 22
(E) 25

Another way to translate into equations:

M - percent discount on one mystery book
B - percent discount on one biography book

B + M = 35
5x20xB/100 + 3x12xM/100 = 19 - the saving of $19 comes from the discounts, which can be directly expressed in terms of M and B, respectively, for the two types of books. Solve the system of two equations: B + M = 35 100B + 36M = 1900 Or: From the answers, we can see that M should be an integer. Because 100 and 1900 are both divisible by 5, only B and E should be checked. Answer E. _________________ PhD in Applied Mathematics Love GMAT Quant questions and running. Director Status: Final Lap Up!!! Affiliations: NYK Line Joined: 21 Sep 2012 Posts: 957 Location: India GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31 GPA: 3.84 WE: Engineering (Transportation) Re: Discounted books in a store [#permalink] ### Show Tags 22 Oct 2012, 08:12 i didnt understand what is (1-b) and (1-m) pls explain in detail VP Joined: 02 Jul 2012 Posts: 1184 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Discounted books in a store [#permalink] ### Show Tags 22 Oct 2012, 08:46 Archit143 wrote: i didnt understand what is (1-b) and (1-m) pls explain in detail An item costs$100.

I am now going to give a discount of b% on it. So my new price would be

$$100 - 100*(\frac{b}{100})$$ $$=$$ $$100*(1-\frac{b}{100})$$

If we take b% in the decimal form. ( eg: 20% as 0.2) then the above equation would be

$$100*(1-b)$$

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A bookstore has a shelf that contains biographies which  [#permalink]

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20 Nov 2015, 01:57
I got the right answer but only after 5 mins. The difficulty is the precision in calculations. How to reduce time on these questions yet still maintain precision?! Thanks very much in advance.
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Re: A bookstore has a shelf that contains biographies which  [#permalink]

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13 Mar 2018, 17:05
1
Anichka wrote:
A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for$12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of \$19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 35 percent, wha is the discount rate on mysteries?

(A) 9
(B) 10
(C) 13
(D) 22
(E) 25

We can let x = the percent by which the biographies are discounted, and thus, (35 - x) = the percent by which the mysteries are discounted. Just as we can express, say, 42% as 42/100, we will express x% as x/100, and, similarly, (35 - x)% is re-expressed as (35 - x)/100. We can create the following equation:

5 * 20 * x/100 + 3 * 12 * (35 - x)/100 = 19

Multiplying both sides by 100, we have:

100x + 36(35 - x) = 1900

100x + 1260 - 36x = 1900

64x = 640

x = 10

Thus, the mysteries are discounted by 35 - 10 = 25 percent.

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Re: A bookstore has a shelf that contains biographies which &nbs [#permalink] 13 Mar 2018, 17:05
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